A166798 Number of nX2 1..5 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.

0, 0, 105, 767, 3160, 9756, 25163, 57293, 118936, 229824, 419277, 729531, 1219856, 1971580, 3094143, 4732313, 7074704, 10363744, 14907249, 21091767, 29397864, 40417532, 54873907, 73643493, 97781096, 128547680

Offset

1,3

Links

Table of n, a(n) for n=1..26.

Formula

Empirical: a(n) = (n^8 + 32*n^7 + 476*n^6 + 3038*n^5 - 1141*n^4 - 35182*n^3 + 53584*n^2 - 25848*n + 5040)/5040.

From G. C. Greubel, May 26 2016: (Start)

Empirical G.f.: x^3*(x^6 + 14*x^5 - 79*x^4 + 108*x^3 + 37*x^2 - 178*x + 105 ) /(1-x)^9.

Empirical E.g.f.: (1/5040)*(5040 - 5040*x + 2520*x^2 + 87360*x^3 + 73080*x^4 + 15708*x^5 + 1414*x^6 + 60*x^7 + x^8)*exp(x) - 1. (End)

Example

Some solutions for n=4
...1.3...2.3...1.2...1.4...1.2...1.4...1.3...1.4...2.4...1.2...1.2...1.1...1.5
...4.2...4.3...4.2...1.4...3.3...2.2...2.3...3.2...3.1...3.4...2.2...1.4...2.2
...4.5...5.1...4.3...2.3...3.3...2.3...4.4...3.2...3.3...4.4...2.3...2.2...3.4
...5.5...5.1...4.5...2.5...4.5...2.5...4.5...3.5...3.5...4.5...5.4...3.5...4.4
------
...2.3...1.4...1.2...1.4...1.5...1.1...1.1...1.3...1.2...1.2...1.2...1.2...1.1
...3.3...3.2...1.4...3.4...2.2...2.3...1.2...3.3...3.3...3.2...5.3...4.3...2.3
...4.1...3.3...3.3...3.4...3.3...4.5...4.3...4.4...3.4...4.2...5.4...5.3...3.3
...4.5...5.3...3.5...5.2...4.3...4.5...4.5...5.2...5.4...5.5...5.4...5.3...5.4

Crossrefs

Sequence in context: A152826 A133767 A166816 * A228303 A033593 A297542

Adjacent sequences: A166795 A166796 A166797 * A166799 A166800 A166801

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved